Algebra 1 Common Core Student Edition, Grade 8-9

Objective To divide polynom ials

Solve a simpler

problem. U se

values fo r r a n d

h to u n d erstan d

what is going on.

Getting Ready!

The large can at the right has a radius

and height th a t are twice those of

th e small can. W hat is th e ra tio of

the surface area of the large can to

th e su rfa c e a re a o f th e small can?

How do you know? (Hint: The formula

for the surface area of a cylinder is

S.A. = 2 7 t t 2 + 2 7 r r h. )

Dividing Polynomials

@ Common Core State Standards

A-APR.D.6 Rewrite simple rational expressions

in different forms; write a(x)lb[x) in the form q(x) +

r(x)lb(x), where a(x), b(x), q(x), and r(x) are polynomials

w ith the degree o f r(x) less than the degree of b(x)...

MP 1, MP 2. MP 3, MP 4, MP 6, MP 7

MATHEMATICAL

PRACTICES in the Solve It, finding th e ratio of th e c a n s’ surface areas involves dividing one

polynomial by another.

Essential Understanding You can divide polynom ials using techniques sim ilar

to th e techniques u sed for dividing real num bers, including long division.

.

How can you change

this problem in to one

you know how to

solve?

Change the division to

multiplication so that you

can use the Distributive

Property.

Dividing by a Monomial

What is (9X3 — 6 x 2 + 15x) 4- 3x2?

(9.r3 — 6x2 + 15x) -T- 3x2 = (9x3 — 6x2 + 15x) •

9X3 6 x 2 , 15 x

3x2 3x2 + 3x

= 3X1 - 2x° + 5x-1

— 3 x — 2 + %

The answ er is 3x - 2 +

M ultiply by the reciprocal o f 3x2.

Use the Distributive Property.

Subtract exponents when dividing

powers w ith the same base.

Simplify.

G o t It? 1. Divide.

a. (4a3 + 10a2 + 3a) h- 2a2

b. (5b4 - 15b2 + 1) ^ 5b3

c. (12c4 + 18c2 + 9c) -h 6c

678 Chapter 11 Rat io nal Expressions and Funct ions